Lecture Notes for Solid State Physics (3rd Year Course 6) Hilary Term 2012 c Professor Steven H. Simon Oxford University January 9, 2012 i Short Preface to My Second Year Lecturing This Course Last year was my first year teaching this course. In fact, it was my first experience teaching any undergraduate course. I admit that I learned quite a bit from the experience. The good news is that the course was viewed mostly as a success, even by the tough measure of student reviews. I particularly would like to thank that student who wrote on his or her review that I deserve a raise — and I would like to encourage my department chair to post this review on his wall and refer to it frequently. With luck, the second iteration of the course will be even better than the first. Having learned so much from teaching the course last year, I hope to improve it even further for this year. One of the most important things I learned was how much students appreciate a clear, complete, and error-free set of notes. As such, I am spending quite a bit of time reworking these notes to make them as perfect as possible. Repeating my plea from last year, if you can think of ways that these notes (or this course) could be further improved (correction of errors or whatnot) please let me know. The next generation of students will certainly appreciate it and that will improve your Karma. , Oxford, United Kingdom January, 2012. ii Preface When I was an undergraduate, I thought solid state physics (a sub-genre of condensed matter physics) was perhaps the worst subject that any undergraduate could be forced to learn – boring and tedious, “squalid state” as it was commonly called1. How much would I really learn about the universe by studying the properties of crystals? I managed to avoid taking this course altogether. My opinion at the time was not a reflection of the subject matter, but rather was a reflection of how solid state physics was taught. Given my opinion as an undergraduate, it is a bit ironic that I have become a condensed matter physicist. But once I was introduced to the subject properly, I found that condensed matter was my favorite subject in all of physics – full of variety, excitement, and deep ideas. Many many physicists have come to this same conclusion. In fact, condensed matter physics is by far the largest single subfield of physics (the annual meeting of condensed matter physicists in the United States attracts over 6000 physicists each year!). Sadly a first introduction to the topic can barely scratch the surface of what constitutes the broad field of condensed matter. Last year when I was told that a new course was being prepared to teach condensed matter physics to third year Oxford undergraduates, I jumped at the opportunity to teach it. I felt that it must be possible to teach a condensed matter physics course that is just as interesting and exciting as any other course that an undergraduate will ever take. It must be possible to convey the excitement of real condensed matter physics to the undergraduate audience. I hope I will succeed in this task. You can judge for yourself. The topics I was asked to cover (being given little leeway in choosing the syllabus) are not atypical for a solid state physics course. In fact, the new condensed matter syllabus is extremely similar to the old Oxford B2 syllabus – the main changes being the removal of photonics and device physics. A few other small topics, such as superconductivity and point-group symmetries, are also nonexaminable now, or are removed altogether . A few other topics (thermal expansion, chemical bonding) are now added by mandate of the IOP2. At any rate, the changes to the old B2 syllabus are generally minor, so I recommend that Oxford students use the old B2 exams as a starting point for figuring out what it is they need to study as the exams approach. In fact, I have used precisely these old exams to figure out what I need to teach. Being that the same group of people will be setting the exams this year as set them last year, this seems like a good idea. As with most exams at Oxford, one starts to see patterns in terms of what type of questions are asked year after year. The lecture notes contained here are designed to cover exactly this crucial material. I realize that these notes are a lot of material, and for this I apologize. However, this is the minimum set of notes that covers all of the topics that have shown up on old B2 exams. The actual lectures for this course will try to cover everything in these notes, but a few of the less crucial pieces will necessarily be glossed over in the interest of time. Many of these topics are covered well in standard solid state physics references that one might find online, or in other books. The reason I am giving these lectures (and not just telling students to go read a standard book) is because condensed matter/solid-state is an enormous subject — worth many years of lectures — and one needs a guide to decide what subset of topics 1This jibe against solid state physics can be traced back to the Nobel Laureate Murray Gell-Mann, discoverer of the quark, who famously believed that there was nothing interesting in any endeavor but particle physics. Interestingly he now studies complexity — a field that mostly arose from condensed matter. 2We can discuss elsewhere whether or not we should pay attention to such mandates in general – although these particular mandates do not seem so odious. iii are most important (at least in the eyes of the examination committee). I believe that the lectures contained here give depth in some topics, and gloss over other topics, so as to reflect the particular topics that are deemed important at Oxford. These topics may differ a great deal from what is deemed important elsewhere. In particular, Oxford is extremely heavy on scattering theory (x-ray and neutron diffraction) compared with most solid state courses or books that I have seen. But on the other hand, Oxford does not appear to believe in group representations (which resulted in my elimination of point group symmetries from the syllabus). I cannot emphasize enough that there are many many extremely good books on solid-state and condensed matter physics already in existence. There are also many good resources online (in- cluding the rather infamous “Britney Spears’ guide to semiconductor physics” — which is tongue- in-cheek about Britney Spears3, but actually is a very good reference about semiconductors). I will list here some of the books that I think are excellent, and throughout these lecture notes, I will try to point you to references that I think are helpful. States of Matter, by David L. Goodstein, Dover • Chapter 3 of this book is a very brief but well written and easy to read description of much of what we will need to cover (but not all, certainly). The book is also published by Dover which means it is super-cheap in paperback. Warning: It uses cgs units rather than SI units, which is a bit annoying. Solid State Physics, 2nd ed by J. R. Hook and H. E. Hall, Wiley • This is frequently the book that students like the most. It is a first introduction to the subject and is much more introductory than Ashcroft and Mermin. The Solid State, by H M Rosenberg, OUP • This slightly more advanced book was written a few decades ago to cover what was the solid state course at Oxford at that time. Some parts of the course have since changed, but other parts are well covered in this book. Solid-State Physics, 4ed, by H. Ibach and H. Luth, Springer-Verlag • Another very popular book on the subject, with quite a bit of information in it. More advanced than Hook and Hall Solid State Physics, by N. W. Ashcroft and D. N. Mermin, Holt-Sanders • This is the standard complete introduction to solid state physics. It has many many chapters on topics we won’t be studying, and goes into great depth on almost everything. It may be a bit overwhelming to try to use this as a reference because of information-overload, but it has good explanations of almost everything. On the whole, this is my favorite reference. Warning: Also uses cgs units. Introduction to Solid State Physics, 8ed, by Charles Kittel4, Wiley • This is a classic text. It gets mixed reviews by some as being unclear on many matters. It is somewhat more complete than Hooke and Hall, less so than Ashcroft and Mermin. Its selection of topics and organization may seem a bit strange in the modern era. The Basics of Crystallography and Diffraction, 3ed, by C Hammond, OUP • This book has historically been part of the syllabus, particularly for the scattering theory part of the course. I don’t like it much. 3This guide was written when Ms. Spears was just a popular young performer and not the complete train wreck that she appears to be now. 4Kittel happens to be my dissertation-supervisor’s dissertation-supervisor’s dissertation-supervisor’s dissertation- supervisor, for whatever that is worth. iv Structure and Dynamics, by M.T. Dove, Oxford University Press • This is a more advanced book that covers scattering in particular. It is used in the Condensed Matter option 4-th year course.